Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
564 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#15690275 | C2 | semidirect |
| 2. C22×C8×D191 | C2 | semidirect |
| 3. C2×#20259302 | C2 | semidirect |
| 5. #27132891 | C2 | direct (N × H) |
| 6. C2×#20259253 | C2 | semidirect |
| 7. C2×#20259247 | C2 | semidirect |
| 8. C2×#102×C191 | C2 | semidirect |
| 13. C2×#15690275 | C22 | semidirect |
| 16. C2×C8×D191 | C22 | semidirect |
| 18. #20259302 | C22 | semidirect |
| 25. #20259253 | C22 | semidirect |
| 26. #20259247 | C22 | semidirect |
| 30. #102×C191 | C22 | semidirect |
| 46. C2×C191⋊C8 | D4 | semidirect |
| 67. C22×D191 | SD16 | semidirect |
| 82. C191⋊C8 | C2×D4 | semidirect |
| 109. C2×D191 | C2×SD16 | semidirect |
| 118. C2×C191 | #465 | semidirect |
| 123. C191 | C2×#465 | semidirect |
| 132. C2×#102 | D191 | semidirect |
| 154. #102 | C2×D191 | semidirect |
| 243. C2 | #27132891 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15690275 | 2 |
| C22×C8×D191 | 2 |
| C2×#20259302 | 2 |
| C2×#20259293 | 2 |
| #27132891 | 2 |
| C2×#20259253 | 2 |
| C2×#20259247 | 2 |
| C2×#102×C191 | 2 |
| C2×#465 | 191 |